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ss7ja [257]
3 years ago
10

Solve for x: log(3x) + log(x + 4) = log(15).

Mathematics
2 answers:
Eduardwww [97]3 years ago
7 0

Answer:

x=1

Step-by-step explanation:

The given equation is

\log(3x)+\log (x+4)=\log (15)

We need to solve the equation for x.

Using the product property of logarithm we get

\log(3x(x+4))=\log (15)            [\because \log (ab)=\log a+\log b]

\log(3x^2+12x)=\log (15)

On comparing both sides we get

3x^2+12x=15

3x^2+12x-15=0

Find factors using grouping method.

3x^2+15x-3x-15=0

3x(x+5)-3(x+5)=0

(x+5)(3x-3)=0

Using zero product property we get

x+5=0\Rightarrow x=-5

3x-3=0\Rightarrow x=1

For x=-5, 3x=-15 and log is not defined for negative values.

It means x=-5 is an extraneous solution.

Therefore, x=1 is the only valid solution of the given equation.

Fed [463]3 years ago
6 0

Answer:

The solutions are x = 1 and x = -5

Step-by-step explanation:

Hi there!

First, let´s write the equation:

log(3x) + log(x + 4) = log(15)

Apply logarithm property: log(3x) = log(3) + log(x)

log(3) + log(x) + log(x + 4) = log(15)

Substract log(3) from both sides of the equation

log(x) + log(x+4) = log(15) - log(3)

Apply logarithm property: log(15) - log(3) = log(15/3) = log(5)

log(x) + log(x + 4) = log(5)

Apply logarithm property: log(x) + log(x+4) = log(x (x+4)) = log(x² + 4x)

log(x² + 4x) = log(5)

Apply logarithm equality rule: if log(x² + 4x) = log(5), then x² + 4x = 5

x² + 4x = 5

Substract 5 from both sides

x² + 4x - 5 = 0

Using the quadratic formula (a = 1, b = 4, c = -5)

x = 1 and x = -5

The solutions are x = 1 and x = -5

Have a nice day!

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7 0
3 years ago
How many solutions does this system have? y = 3 x minus 5. y = negative x + 4. one two an infinite number no solution
AveGali [126]

Answer:

One

Step-by-step explanation:

It is given that,

y = 3x-5 ....(1)

y = -x+4 .....(2)

We can solve the above equations using substitution method. Put the value of y from equation (1) to equation (2) such that,

3x-5 = -x+4\\\\3x+x = 5+4\\\\4x = 9\\\\x=\dfrac{9}{4}

Put the value of x in equation (1) we get :

y = 3x-5\\\\y = 3\times \dfrac{9}{4}-5\\\\y=\dfrac{7}{4}

It means that the value of x is \dfrac{9}{4} and the value of y is \dfrac{7}{4}. Hence, the given equations has only one solution.

6 0
2 years ago
Nwhat is the range of data set for 8 1 7 6 14
bazaltina [42]

Answer:

14-1=13 range= 13

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set. To find the range, first order the data from least to greatest. Then subtract the smallest value from the largest value in the set.

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Allen is buying a video game that originally costs $49. He has a 10%-off
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3 years ago
Clare went to a concession stand that sells pretzels for $3.25, drinks for $1.85, and bags of popcorn for $0.99 each. She bought
djyliett [7]

Answer:

No.

Step-by-step explanation:

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Price of two pretzels = $3.25 \times 2 = $6.5

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The money spent when 2 pretzels, 2 drinks and 2 bags of popcorn are bought is $12.18.

But maximum money available is $10.

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